Definition of terms for a Synchronous Current-mode Buck Regulator?
You haven't supplied a link to the datasheet, so I'll only answer in general.

Synchronous is a common term in switching power supplies, and is short for synchronous rectification.  In a basic buck switcher, there is a diode from ground to the input of the inductor.  That works, but adds a diode drop of extra voltage across the inductor to "discharge" it more quickly than the output voltage requires.

The synchronous trick is to add a FET across the diode, and turn the FET on when you know the diode is supposed to conduct.  That decreases the voltage drop, making the whole converter more efficient.  The downside is that things go bad fast if this FET is ever turned on when the diode would not otherwise conduct.  This is why synchronous rectification is something you have to wake up to design, unless you just buy a chip with it already incorporated.

Current mode is the name for one of the various possible control schemes of a switching power supply.  This is mostly irrelevant to you when just buying a chip.

There is a controller in the chip that tweaks something to maintain the output voltage at the desired level as the load changes.  In a switcher, there are various things that can be tweaked, like the pulse width, pulse frequency, and others.  Current mode control is a particular scheme that decides to end each pulse when the inductor current has built up to a specific level.  This reference level is what the controller tweaks in order to keep the output voltage at the desired value.

As with all control schemes, this has advantages and disadvantages.  Current mode control simplifies the compenstation network, but that requires too much math to explain in this answer.