What is sea level?
What is sea level? Where is "zero feet sea level"? Who decided that a particular place was to be considered zero, instead of some other place, such as Lake Titicaca? And what time of day can "zero" be read at the designated place (you know, what with tides and all)? How can zero be plotted around the globe, to, say, the Rocky Mountains, where there are no zero locations, with any accuracy? And what difference does it make, anyway?
What, you want the people in the Federal Sea Level Research Bureau to get fired and starve? Fact is, sea level is a mighty handy concept.
There isn't any particular place at which sea level (mean sea level, to be precise) is measured. It's strictly an average.
Sea level is based on the assumption that because the oceans are interconnected and water tends to find its own level, the ocean surface around the world forms an ellipsoid (or flattened sphere, which is what shape the earth is) of more or less uniform geometry, once you average out the tides and seasonal variations over a long period, typically 19 years.
That makes sea level a useful reference point in calculating elevation, which makes a big difference in climate. In fact there are some permanent differentials in ocean level amounting to about a meter or so due to currents and whatnot, but we can ignore them for now.
Because the ocean surface serves as a floor for the atmosphere and because atmospheric pressure decreases predictably with height, you can use a barometer to establish the elevation of any inland landmark, once you've corrected for local climatic variations. (Elevation can also be established by ground and satellite-based surveying.)
Then--and here we get to the important part--you can mark the elevation on the charts distributed to airline pilots. If the altitude of an airliner (as shown on its barometer-based altimeter) fails to exceed the elevation of the spot it's flying over, big-league problems will result. So you better hope when they figured out mean sea level that they did their arithmetic right.