32bit float is 24bit (mantissa) with the ability to scale by 8bits (exponent), so that using floating points means that intermediate summing points can exceed normal digital full scale that would otherwise overload a DAC, which must always have an input below full scale.
The downside is that resolution in arithmetic suffers when values are not in the same range. Using decimal to illustrate, subtracting 0.84 from 1.5 results in 0.7. Both have two digits of resolution, but the result only has 1 digit, because the least significant digit of the lesser value is ignored as it has no corresponding digit in the larger.
Of course, with 24bits of playroom, a single calculation is of no consequence as the lower bits are buried in the noise floor in the end. The problem comes when there are thousands or millions of calculations, because errors accumulate, especially for reverb, where results feed back into the next round of calculations. This all gets worse when the starting values are lower than full scale.
For this reason, some digital mixers use 48bit integer internal values, and some DAWs, like ProTools 11, use 64bit floating (known as double-precision, and it uses 53bits+11bit exponent), to provide extra ‘guard’ bits. These large precisions are overkill for audio, but some are what CPUs provide hardware support for besides 32bit (single-precision) floating, which results in significantly lower calculation times than if they were done in software at lower resolutions.