ἀπόλλῡμι I lose; I destroy, ruin

Why are they called -μι verbs?
Because the first person singular, the "I" form ends, not in our well-known -ω, but in -μι. Compared to most languages, Greek verbs are a whole lot easier - in the present tense that is.

1. -ω verbs, including the dreaded contract verbs in Attic Greek (-ῶ)
   They are also called thematic verbs because they insert a thematic vowel between the stem and the personal ending. For ease of pronunciation it combines with the personal endings, that is why we haven't mentioned it before. Cf. the table lower down, comparing thematic omega verbs and athematic -mi verbs.
2. -μι verbs:
   also called thematic verbs because the personal endings are added directly to the stem. There is no need for an extra vowel because the stem of any -mi verb ends in a vowel.
       -υμι,
       -ημι
       -ωμι

Compare:

So here (lesson 10b, supplementary Reading) we have:
Odysseus loses his companions, i.e. the rest of them, the ones that haven't been eaten by Polyphemos the Cypclops, by Scylla the 6-headed sea monster etc. etc.

I personally οὐκ ἀπόλλυμι many things, and when I do, I usually εὑρίσκω αὐτά quickly enough.
Whereas my friend αἰεὶ ἀπόλλυσι τὰ πάντα ἀλλὰ οὐχ εὑρίσκει οὐδέν οὔποτε (doesn't ever find anything: the Greeks say: not finds nothing never. When they think negative, they use negative. As often as it takes! Just like the French, Spanish, Portuguese, Russians...).
ἐν τῷ πέμπτῳ μαθήματι ὁ Φίλιππος ἀπόλλυσι τὸν κύνα ἐν τῷ ὄρει.
What about you? ἆρ' ἀπόλλυς ἀργύριον; χρόνον; τὸν κύνα ἐν τῇ πόλει;
What about your wife/husband? ἆρ' ἀπόλλυσι πολλά;
What about your children? ἆρ' ἀεὶ ἀπολλύασι τὰ πάντα ἢ οὐ;

The verb to be is also a -μι verb, obviously, though an irregular one.