Learn Russian: Это моя семья.

Моя is the feminine version of 'my'. Because семья (family) ends in -я, it is a feminine noun. Possessive pronouns must always match the gender of the thing they belong to, so we use the feminine моя instead of the masculine мой.

If семья is feminine, why doesn't это change to match its gender?

When you use это to mean 'This is...' or 'These are...', it acts as a fixed introductory word. It always stays это, no matter if the noun that follows is masculine, feminine, or plural. You only change the gender of 'this' when it attaches directly to a noun, like 'this family' (эта семья).

Where is the word for 'is' in this sentence?

Russian doesn't use a word for 'is' or 'am' or 'are' in the present tense. You literally just say 'This my family' (Это моя семья). You only add a 'to be' verb if you are talking about the past or the future.

What does the soft sign (ь) do in the middle of семья?

The soft sign (ь) doesn't make a sound by itself, but here it acts as a separator. It tells you to pause slightly and pronounce the м and я distinctly, keeping the 'y' sound of the я clear (sem-YA). Without it, the letters would blend together differently.