We can draw the curve of a function of one variable, showing the values that the function takes as we vary the input.
If a function depends on two variables then instead of a curve the function has a surface.
We can plot the function as a three-dimensional picture, showing how it changes as either of the variables changes. The pictures below help to illustrate what I mean.
Consider the function z(x,y)=2x+3y. To start trying to draw this, we'll just think about how z depends on x, for a fixed value of y, say y=0. For y=0, the function is just z=2x. That allows us to draw the following picture:
In that picture, the x and y axes are both horizontal, with the y-axis going into the screen, and the z-axis is vertical. Just the line z=2x has been drawn, for y=0.
Now we'll do the same for the z-y relation. We put x=0 and get z=3y. That gives us the following picture:
Because the function 2x+3y is linear, the surface in this case is a plane, that is a flat (but probably sloping) surface. That's the two-dimensional equivalent of the straight line that you get for a linear function of one variable.
To draw this plane, we can join up the two lines we found above, to get:
Now recall the function we had earlier, f(t,x)=tsin(x). This function is linear in t, so the cross-sections of the surface in the t-direction will be straight lines as in the previous example. However, the function varies like a wave in the x-direction, so for (almost) any value of t that we choose, we should end up with a wavy cross-section in the x-direction. Here's the surface in this case:
The variable t is increasing as you move from left to right. So at the left-hand end of the surface where t is zero, the surface is flat, the function tsin(x) is zero for all x. Then as t increases, the waviness becomes apparent, and you can see that any cross-section at a fixed value of t will give a sine curve.
If instead you cut the surface parallel to the t-axis, at a fixed value of x, say x=x0, then the curve you'd see would just be a straight line, with constant slope sin(x0), with the function given by f(t,x0)=t sin(x0).
So for example, in the picture (shown again below for convenience) you can see that the cross-section in the right-hand end of the box is a sine wave, in fact it's f(3,x)=3sin(x). Similarly, the side of the box nearest to you shows a straight-line cross-section. Here x=-5, so the function is f(t,-5)=sin(-5)t, and since sin(-5) is about 0.96, the function is roughly f(t,-5)=0.96t.