My own approach to this was to use what I believe is a Brainstorming technique: if you're having trouble defining or grasping a word, ask "What is its opposite?". For me that had an immediate answer - the opposite of meekness is arrogance. And the essence of arrogance seems to me to be that it ignores legitimate boundaries. Arrogance takes what it wants, whether there are legitimate obstacles in its way or not. It assumes rights or authority it does not have, ignores legitimate authorities who would oppose it, and ignores the rights of others when those rights get in the way of what it wants.
Well, if the essence of arrogance is that it ignores legitimate boundaries, it seems likely that the essence of meekness is that it instead respects them. This is a definition (or at least description) that I can get hold of. The meek person can be strong, even bold and assertive, but it stops when it comes up to a legitimate boundary or restriction. It allows its strength to be limited by legitimate laws, rules, or authorities. I've heard meekness defined as 'strength under control', but it seems to me that that is mere self-control(to what degree self-control can really be considered 'mere'. We could use seeing lots more self-control). A meek person allows himself to be controlled by legitimate outside authorities, not just by himself.
Make no mistake, even this kind of meekness seems 'weak' to the arrogant. The failure to take what you want, regardless of rules is regarded by the arrogant as a character failure and a sign of weakness. You can expect to have some people still regard you as weak when practicing this kind of of meekess. But their disdain is not itself a legitimate restriction, and shouldn't be regarded as one.
You've probably noted the heavy usage of the term 'legitimate' in the above. The meek won't necessarily allow themselves to be limited by restrictions that aren't valid, though they are free to allow that and beyond ("if someone wants to take your coat, give him your shirt also") or to go beyond legitimate restrictions ("if someone forces you to go a mile, go with him two". But they are also free to ignore restrictions that are not legitimate or to require others to respect legitimate restrictions (see Paul in Acts 16:37)
And this type of meekness seems to me to make the Beatitude understandable. Jesus says of the meek, not that they will acquire the earth, nor that they would conquer the earth (that would be more what the arrogant aim for), but that they will inherit the earth. The earth is handed over to them by someone else. And I suspect that it's handed over to them simply because they can be trusted with it. They won't take it as an indication of authority beyond what they actually have, they won't abuse it, they won't use it selfishly. They will not go beyond proper boundaries in using it, and they therefore can be trusted with it. The arrogant may think the earth is going to be theirs, but God controls the earth, and will ultimately give it to those He knows can be trusted with it (and it will probably drive the arrogant crazy!)