Learn Finnish: Kotka avaa siipensä, kun se on iskemäisillään. - The eagle opens its wings when it is about to strike.

It uses the fifth infinitive, which expresses being "just about to" do something. You take the strong vowel stem of the verb (iske-), add the fifth infinitive marker -mäisillä- (using ä instead of a because of vowel harmony), and finish with a possessive suffix. For the third person ("it"), the suffix here is a vowel lengthening plus -n, giving us -ään.

Does siipensä mean "its wing" or "its wings"?

In this sentence, it means "its wings" (plural), though grammatically it looks identical to the singular. When you add a possessive suffix to a nominative plural word (which normally ends in -t, like siivet), the -t drops out. Therefore, both siipi + nsä and siivet + nsä become siipensä. Common sense tells us an eagle opens both wings!

Could I just say kun se aikoo iskeä instead of using this complex fifth infinitive?

You could, but it loses the immediate intensity of the moment. Aikoa means "to intend" or "to plan", so kun se aikoo iskeä just means "when it intends to strike." The fifth infinitive iskemäisillään means the eagle is "on the verge of striking" or "at the very point of striking"—a split second before the impact happens.

Is iskeä the standard verb for an animal attacking?