It sounds to me like you're creating a feedback loop. Basically this happens when the sounds coming out of the speaker is being reflected back into the microphone (which in turn boosts the sound coming out of the speaker which causes even more to be picked up by the microphone and so on). Just try adjusting the position of the phone or if you're using some sort of handless set make sure the microphone portion is not in the path of the speaker portion
Neither of these explanations are satisfactory; turbo-1, you have given a necessary but insufficient condition for terminating the self-echo (i.e. I doubt springBreeze has their speakerphone on, or at least I have had this phenomenon happen to me without the speaker phone on). Maverick, the effect you have described does not apply to this mystery because a necessary precondition for such a feedback loop to form is that my voice come out of my phone's speaker, and so if this were the explanation then the effect would precede the cause.
Examination of Maverick's hypothesis shows that the echo could be due to your voice coming out of the speaker of the phone of the person you are talking to and entering their microphone, thus being sent back to your earpiece. I'm sure this is what he/she meant to describe. If this is the cause of the echo then the problem cannot be solved by adjusting the position of your phone, but rather must be solved by the person you are talking to having to adjust their phone.