A checking account in a foreign bank is considered a foereign financial asset?

Yes.

It's a foreign financial asset for determining the threshold for form 8938 and the FBAR.

What are the thresholds?

For form 8938, the thresholds are given on page of this IRS document. 

For the FBAR, you'll need to file if the total of your foreign bank accounts exceeds $10,000 at any time during the tax year.