The FTSE 350 index tracks UK blue-chips and mid-caps. It's constituents are the shares of companies in the FTSE 100 and the FTSE 250.
It is a wider index than the FTSE 100 and is a slightly better indicator of the market as a whole but it is not as widely followed or as well publicised. With about 90% of the market cap of the 350 coming from FTSE 100 companies there is rarely much difference between the two indices.
The index value is calculated using the same methodology as the FTSE 100 and 250, and the selection of constituents is obviously the same.