What is the significance of the DFT in SC-FDMA systems?
In the LTE uplink, user equipments (UE) of different users share the same frequency band when sending data to the base station (BS). This frequency band is divided into smaller resource units which must be used by only one UE at a time. This technique is called frequency-division multiple access (FDMA).

Let's first assume that there are $M$ UEs and that every UE uses conventional orthogonal frequency division multiple access (OFDMA). That is, every UE has an IDFT block of length $N$. Different UEs must not use the same subcarriers at a time so their transmit data is distributed onto orthogonal sets of subcarriers. 


  Example: Let $N=30$ and $M=3$. To implement FDMA we could assign
  subcarriers 1 to 10 to UE1, 11 to 20 to UE2 and 21 to 30 to UE3.


The drawback of this technique is that the resulting transmit signals have a relatively high peak-to-average power ratio (PAPR).

The prinicple of SC-FDMA is to generate (in every UE) a single-carrier signal and to shift this signal to the frequency resource that is assigned to the respective UE. The necessary frequency shift is implemented by the $N$-IDFT. The three principal blocks are:


DFT: Take $M$ QAM symbols $y(n)$ (which can be interpreted as $M$ consecutive symbols of a single-carrier signal) and calculate the frequency-domain representation $Y(k)$ of this signal by an $M$-DFT.
Subcarrier mapper: "Place" $Y(k)$ in the freq. domain at the freq. resource that is assigned to the UE. This is done by assigning $Y(k)$ to the  $M$ IDFT inputs that represent the wanted freq. resource and by setting the remaining $N-M$ IDFT inputs to zero.
IDFT: Calculate the time domain signal.



  Example: Again, $N=30$, $M=3$. In every UE, calculate the DFT of $N/M=10$ QAM transmit symbols. In UE1, assign the result to IDFT inputs 1 to 10. In UE2, assign the result to IDFT inputs 11 to 20. In UE3, assign the result to IDFT inputs 21 to 30. The remaining IDFT inputs are set to zero, respectively.


The DFT makes SC-FDMA a single-carrier signal because the input to the IDFT is a "spectrum" already not QAM symbols. Therefore, the result of the IDFT is a frequency-shifted single-carrier signal.

I'd like to point out, that the whole purpose of SC-FDMA is to reduce the PAPR. Especially, SC-FDMA is not necessary to implement FDMA. This can also be done by OFDMA.

Also, there are different subcarrier mapping schemes. In my answer I have assumed the so-called localized FDMA (LFDMA) which assigns $Y(k)$ to neighbouring IDFT inputs. Another technique is the interleaved FDMA (IFDMA) which assigns $Y(k)$ to IDFT inputs with distance $M$ in an interleaved way. It has an even lower PAPR. The PAPR of OFDMA, LFDMA and IFDMA are compared in [1].



[1] Myung, H., Lim, J., &amp; Goodman, D. (2006). Peak-To-Average Power Ratio of Single Carrier FDMA Signals with Pulse Shaping. 2006 IEEE 17th International Symposium on Personal, Indoor and Mobile Radio Communications