Yes, originally MPLS technology was to provide better forwarding performance by using tag switching. This because making forwarding decisions on a fixed sized address field (like MAC) doesn't require the hardware resources that making a forwarding decision on a variable sized address field (like IP) does. However, although later hardware technology has very much narrowed the performance gap, it's still somewhat present. Yet, besides the performance benefit, the usage of MPLS labels allow "doing things", also at hardware speeds, that would not be possible without the additional MPLS label. (Basically, MPLS labels allows them to be used to retain information beyond a tag for a destination. For example, MPLS allows the same IP address, to be used in the same physical network, yet kept separate, somewhat the L3 version of a L2 VLAN.)
Traffic engineering is a way to use MPLS to direct some MPLS traffic to flow the way you want, i.e. not follow routing's "best path". (It's somewhat an advanced static routing and/or PBR, often on top of networks using BGP.)
