There are two levels of Dual SIM support. Dual SIM Dual Standby (DSDS) and Dual SIM Dual Active (DSDA).
The basic difference is that with DSDS when you have an active connection with the network on one SIM, you cannot have an active connection using the other SIM. To the network, it's like that connection is non-existent, and for instance an incoming call cannot make it to your device at all, and would go to voicemail automatically.
It's common for DSDS devices to provide optional automatic call forwarding on the other SIM when they establish an active connection, so that calls to your other SIM will be diverted to your active connection SIM giving you the option of picking up via call waiting.
DSDA devices could have active connections simultaneously.
DSDA devices require two radios internally, which is why they're far less common.
The Snapdragon chipsets could support either mode, but would require second radios to support DSDA. According to the specifications released, the 950 and 950 XL support DSDS, not DSDA.