Here are some examples with explanations.
"From this aspect the house looks smaller." Here aspect means literally what you can see from where you are looking. Looking at a house from down the street is a different aspect than looking at it from above.
"One aspect to the issue of poverty is homelessness." Here aspect basically means it is one part of it.
"From one aspect this story seems like a woman being kind to a stranger, but from another aspect it could be a stranger taking advantage of a woman." Here aspect means it is two ways of thinking about the same thing.
"How does the painting look from your aspect?" "from your aspect" generally just means "your opinion", as it does here.
Basically these can all be summed up as "a particular way of seeing/viewing/thinking about something"