At least in principle any load can be moved by a lever. A lever is a rigid uniform rod resting on a fixed point called fulcrum at which point it can rotate freely. The length of the lever from this fulcrum to the load is load arm and the length from fulcrum to the point where effort is applied is the effort arm. The lever is balanced when Effort x effort arm Load x load arm. If the effort arm is 100m and load arm 1m, the effort needed to lift 1000 kg will be just 10 kg. So keeping the effort arm proportionally long one can in priciple lift any load and that is what Archimedes was trying to say by this boastful statement.
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