Gamma rays are very high frequency waves which are produced by radioactive decay whereas alpha and beta particles have lower frequencies. As a result, gamma rays have much higher energies as compared to alpha and beta particles. Hence, gamma rays have much higher penetrating abilities than alpha and beta particles. In fact, gamma rays can only be stopped with a lead shield of a few cm thick as compared to alpha and beta particles which can be stopped by paper and thin foil respectively.
Alpha particles are the nucleus of the helium atom, and really heavy compared to beta particles which are electrons. Alpha particles are quite easy to stop as Daphne says, beta particles take a bit more effort but gamma rays are very high energy electromagnetic radiation and hard to stop. It takes a lot of stuff to remove all the energy they have.
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