They Army keeps changing the size of their units so it is a moving target, but it works something like this
A MEU is a forwardly deployed - generally amphibiously - Unit of roughly a large battalion size (1000+ riflemen,) plus there may be an Armor attachment, and there will be and organic air unit that may contain fixed wing elements plus an organic support unit ("organic" is a buzzword for "self contained.") The MEU is an expanded "battalion" with cross arms, air and support. Typically a deployed MEU will have 2000 to 2500 marine altogether, plus the sailors on the ships. I do not know the current size of an Army battalion but is used to be arond 1000 soldiers, with no organic support.
A MEB (Marine expeditionary Brigade) is the next larger unit and is composed of usually of 4 MEUs. MEBs can be deployed amhpibiouly or in a combination of Air, Land and Sea, deployement. A MEB is generally the largest unit that one can consider to be "Fleet Marines" (i.e. "deployed with the fleet.) They extrememly large Army brigade (again with organic cross arms, air and support) or a army division.
A MEF (Marine Expeditionary Force) is made up of three MEBs (I think that once upon a time there were 4 MEBs to a MEF.) Another way to think about it is that MEF is made up of a Marine Divsion (a MARDIV which is much larger that an Army Division) an Air wing (fixed and rotary,) a Armored full brigade and a support unit. I think that these days a MEF is around 45,000 all told.The USMC is made up of 3 MEFs and the size of the Corp is roughly 170,000 including reserves (MEFIII is a reserve MEF,) which would seem about right if you subtract out Marines on other duties like embassy work, etc. Each MEF at any one time has 1 active, generally deployed MEB, one MEB in training and one MEB refurbishing itself from the last deployement. Sadly, each MEF as only enough ships to sea deploy only one MEB at a time. So you see a MEF is larger than an Army Division
In combat the is a higher structure called a MAGTF (Marine Air Ground Task Force) which is quite mallebleable in deployment - It could be two MEUs or or it could be all three MEFs.
Some of this is hard to make out because the USMC is structured for very quick deployment and so has a very "adaptable force structure" It can "cut and paste" units for a particular mission. It may in fact draw from each MEF the Units that make up a deployed MAGTF. The USMC does not have the notion of "historical Units" that the army has, And infact one rarely seea unit patches r insignia for these units, and Marines do not wear unit patches on their uniforms.
It also gets complicated in that there are "administrator Units (Divisions, Brigades, Marine Regiments, etc) and deployed units (MEUS, MEBs Etc.)
The USMC is a quite unique military force, though some of the new organizational structures the army is thinking about are similar (I will not say that they are copying them because I do not want the flames.)