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you want me to give you a philosophical answer? or just p=mv? i'll think a little bit on that one.
in your own words
ok, this is a bit difficult. most physical concepts have been first defined mathematically and then "explained". For example, you could have also asked, what is force? but force is just F=ma. momentum is a bit like energy; it is something that is stored by an object as it gains speed. But its mass also has a factor: if I weighed 200 lbs and were going at a speed of 4m/s, I would have more "moving energy" than someone who weighed 100 lbs and were going at the same speed. in essence, it is still the characteristic of someone's speed combined with his mass. basically, scientists have a funny way of associating qualities. I think they got the idea that both mass and speed had an effect on an object when one object hit another one, so they basically took the two quantities and multiplied them. in short, momentum is "a quantity that takes into account both the effects of mass and velocity"
later on, (or maybe already), you will have learned that F=(p-p0)/t. if you have ever heard something like "...hurling a ten-pound ball going at 100 miles per hour at me" you may have imagined what it would be like to see it... that idea would be momentum, and the pain that you feel afterwards would be force (F) =D hope that helps
don't worry, i took a bit of time myself to come up with a philosophy like that when I was in first year physics. If you have more questions, ask.
about the multiplying random quantities associated with characteristics: I didn't make that up. when you go on to magnetism and electricity and all that fun stuff, you'll realize that my statement is more true than it seems. (for example: torque is the cross product of position and force)