Standing is an adjective & a noun. Adjective: Standing water, standing army, standing game (like every Thursday), standing invitation.
Noun: She's in third place in the standings. A member in good standing.
However, grammar is not my area of expertise.
You'd think it would also be a verb but it's listed as stand not standing. (very weird).
"Standing +" Up/on/over/ (a preposition) could be the verb, but someone who is more knowledgeable would have to answer why it's also not listed as a verb in the first place.
Because it's: a woman stand. (This is a tricky English thing). It normally should be: a woman stands. But it's actually supposed to be in this particular phrase: I see a woman stand. If this is the whole sentence, "stand" is a verb. If you were trying to say you see her standing in general (like not doing anything but upright in a location), it's "I see a standing woman." You could also just add words (adverb or preposition) after stands: A woman stands there. I see a woman standing in the corner. It's a weird word now that I think about it. For examples of the difference see: http://learnersdictionary.com/definition/stand
If you are not a native English speaker it's probably best to watch, listen or read things in English to understand the differences. It can be confusing.