dBm is a log unit, so yes, a less negative number actually means the signal is stronger, for instance a -50 dBm signal would be stronger than a -60 dBm signal. It's not likely to see higher than around -40 dBm in any real world environment, and you'd only see that very close to a cell phone tower.
For a more technical explanation, any number in dB is actually just a relative quantity referenced to some established value. In the case of dBm, the reference value is 1 milliwatt. Mathematically, the relationship is 20*log(power in milliwatts) = power in dB; because a log function is involved, any input values less than 1 (typically, the power received by a cell phone is several orders of magnitude lower than a milliwatt) will result in a negative output. For example, if your phone is receiving a -80dBm signal, it's antenna is receiving .0001 mW, or .1 uW. An easier approximation is that for every 3 dB difference, the value in reference units changes by a factor of .707, so where -80dBm is .1 uW, -83 dBm is .0707 uW, and -77 dBm is .141 uW.
