lw (load word) loads a word from memory to a register.
lw $2, 4($4) # $2 <- mem($4+4)
$2 is the destination register and $4 the address register. And the source of information is the memory.
4 is an offset that is added (not multiplied) to the address register. This kind of memory access is called based addressing and is it quite useful in many situations. For instance, if $4 hold the address of a struct, the offset allows to pick the different fields of the struct. Or the next or previous element in a array, etc. offset does not have to be a multiple of 4, but (address register + offset) must and most of the time both are.
Sw is similar, but stores a register into memory.
sw $5, 8($7) # mem[$7+8] <- $5
Again $7 is the register holding the memory address, 8 an offset and $5 is the source of the information that will be written in memory.
Note that contrary to others MIPS instructions, the first operand is the source, not the destination. Probably this is to enforce the fact that the address register plays a similar role in both instruction, while in lw it is used to compute the memory address of the source of data and in sw the memory destination address.