1. I wrote a letter.

2. I have written a letter.

What is difference between these two sentences?

I know that 1) is in simple past tesnse and 2) is persent perfect.

But, both as I think suggest that work has completed in past.

Please explain a bit to clear the usage of simple past and Persent perfect tense.
There is more than one difference between the simple past and the present perfect. The simplest difference is the grammatical difference that the simple past can be used with expressions which signify a definite, particular time in the past.

I wrote a letter yesterday.
I wrote a letter at 7 o'clock.
I wrote a letter last Monday.
I wrote a letter several weeks ago.

The present perfect cannot be used with such expressions. (After all, it IS a "present" tense!)

I have written a letter yesterday. (wrong!)
I have written a letter at 7 o'clock. (wrong!)
I have written a letter last Monday. (wrong!)
I have written a letter several weeks ago. (wrong!)

Being a "present" tense, the present perfect can be used with "now":

I have now written a letter.

Another difference is the way the two tenses "cut through time". Imagine time as a very, very long loaf of bread extending into infinity from where you are located. As you look into the distance at this long loaf of bread, let's say that you are looking into the past. The loaf ends at your feet and this is the present moment.

When the simple past tense is used to report an event, it "cuts a slice out of time". To do this, somewhere along the bread loaf ( time ) you make two cuts, fairly close together. The cuts represent the beginning and the end of the event or action. Suppose you wrote a letter. It took, let's say, an hour. Then the thickness of the bread slice represents one hour of writing. If that hour took place this morning, the slice is located quite close to you: "I wrote a letter this morning". If that hour took place yesterday, the slice is located farther from you: "I wrote a letter yesterday." If it took only 15 minutes to write the letter, the bread slice is much thinner, but again the slice may be closer to or farther from the present (e.g., this morning or yesterday).

When the present perfect tense is used to report an event, the "slicing" is different, because you don't know exactly where the slice is located along the loaf. If you say "I have written a letter", you know there were two cuts in the loaf to make the slice, but you don't know where. You only know that if you examine the loaf, you will discover a slice representing the letter writing somewhere along the loaf. Another feature of the present perfect is that you can limit how far back in time - how far back along the loaf - you want to go in your search. This is done with a "since" clause. In the sentence "Since Monday, I have written a letter", we know that the slice representing the letter writing will be found between the distance from us which represents Monday and the present moment (at our feet). But we still don't know exactly where within that more limited part of the loaf we will find the slice.

Another way to look at it is that the simple past "singularizes", "individuates", or "particularizes" an action by focusing on a specific time. Whether the specific time is mentioned or not, the simple past, when used to report an event, always implies "at a certain time". In fact, it is this implication that particularizes the event. Even if the implication is "when it happened", the implication is still there. "Did you see that?" implies "Did you see that when it happened?" Another example: "Did you notice that John got nervous when we mentioned the missing cash?" The noticing we are referring to is the noticing of that specific instance of nervousness that occurred at the time we mentioned the missing cash.

The present perfect, however, does not "singularize", "individuate" or "particularize" an action. With the present perfect, we don't even know exactly when the action happened! What is more important with the present perfect is that the action now has some felt effect on the present. When you say "I have written a letter", in a way you are pointing to that letter and saying, "And here it is. Here is the letter I have written" -- even though the pointing and saying may be only a mental pointing and saying! The important thing is having (hence the auxiliary "have") the letter now.

Another way to look at the present perfect is that it is the "diary tense". It is as if everyone has an imaginary diary where his life experiences are written. With "I have written a letter" we are saying that we will find in your "diary" today, - if we look now - the notation: "Letter - written!" on some page of the "diary", but we don't know or don't care which page that might be.

Becoming adept at the use of the simple past and the present perfect takes lots of practice. Don't be too disappointed if you find it difficult at first. Emotion: smile
Dear Jim,

Your posts are always very useful and informative. I knew the difference between Simple past and Present Perfect. But your bread-example made it very clear to me. You are really a great source of knowledge for me. I always learn many new things from your posts.

Thanks a lot!