Sampling Theorem illustration
This plot depicts how to convert your digital signal back to the analog one, using $\mathrm{sinc}$ functions. The nice property of these functions used in this process, is that maximum of each function always occurs at minimums of the other, shifted function:



Now the process of the D/A conversion that is depicted on your plot is basically taking a $\mathrm{sinc}$ function, and multiplying it by one sample that is at the maximum of $\mathrm{sinc}$. You do it for each and every sample of your digital signal, and then sum all of the outputs. For example, for the above plot, the outcome would be following:





Now maybe some more complicated example of D/A conversion. On the plot below, you can see the actual samples (in blue) and "analog" $\mathrm{sinc}$ interpolated signal (in red).



Plotting each function separately you can observe what will become an analog signal later:



I hope that it is more intuitive for you now. In order to complete this example, here is some MATLAB code I used:

clc, clear all, close all
fs = 32;
dt = 1/fs;

% Generate a samples of the signal
ts = linspace(0, 1, 10);
s = 2*sin(2*pi*ts) + sin(2*pi*3*ts);

td = linspace(0, (length(s)-1)*dt,     length(s));
t  = linspace(0, (length(s)-1)*dt, 100*length(s));

sincM = repmat( t, length(td), 1 ) - repmat( td', 1, length(t) );
SS =  s* sinc( sincM/dt );

% Sampled signal
stem(td, s, 'b', 'linewidth', 2)
hold on
% Reconstructed signal
plot(t, SS, 'r', 'linewidth', 2)
grid on

legend({'sampled signal', 'interpolated signal'})

figure 
stem(td, s, 'b', 'linewidth', 2)
hold on
grid on
% Each sinc function
basis = sinc(sincM/dt)';
sbasis = bsxfun(@times, basis, s);
plot(t, sbasis)