National president of BJP's minority cell Tanvir Ahmed, who was here on Friday, said that all its units across the country would participate to make the bandh successful.

"Inflation affects one and all. The fuel price hike has only further added to the financial burden of the common man," he said while ad-dressing a press conference.

He added that the UPA government has failed in governance, especially in controlling inflation. State president of the cell Mumtaz Bhati was present on the occasion.

Ahmed said the party is now focusing on strengthening the cell. "We are concentrating on increasing our strength at the grassroots level and aiming at more participation from the minority community at the block and district levels," he said.

Please explain to me the emboldened parts. Though I guess "grassroots level" means "ordinary man/public" and "block" means "area that is ruled by a party".

Source : http://timesofindia.indiatimes.com/City/Jaipur/BJP-gears-up-for-Bharat-Bandh/articleshow/6122751.cms
This appears to be a specialized meaning of "cell" used only in the political system of India. Presumably it is a group of people working together toward common goals, possibly elected officials, possibly appointed officials.

The grassroots level is at the level of individual citizens. You're right about that. The term "grassroots" is used in the U.S. as well.

It is clear that within the political hierarchy the block level is smaller than, and probably reports to, the district level. I assume the various levels are defined by the political parties themselves, so to understand this material well, you would have to study the political parties of India in greater detail.

National president of BJP's minority cell Tanvir Ahmed,

This is "the cell." A cell is simply a group of people with a common purpose. In this case, they're a minority group. The sentence seems to suggest that this cell comprises the total membership of the political group, since T. A. is their National president.

The term "cell" is sometimes used to describe a small organized group of foreign agents, or sabateurs, living anonymously in a given country. (Not in this case!)

Didn't we do "grassroots" before?

at the block and district levels,

In large cities in the US, political parties often form political organizations within each city block, in order to help promote their candidates. Political districts would be the next larger geographic areas.

The expression "grass roots" refers to the process of catering to the needs and wishes of the common people.