What you are missing is the concept of rotational speed. This is required to fully understand the relationship between horsepower and torque.
We'll start with the concept of torque. Torque is simply defined as the rotational force of an object on an axis. This is easily calculated as T = R x F, where:
T = Torque
R = Position Vector (Essentially the distance from origin point to where force is being applied)
F = Force Vector
Angular velocity is simply the rotational speed of of an object on its axis and is measured by rotational distance over time, such as radians or degrees per second. RPM (Revolutions per minute) is a unit of measurement of how many full revolutions (360 degrees) an object makes over time.
Horsepower is an imperial unit of measurement regarding power. It is described as 550 ft-lbs per second, or 33,000 per minute to equal 1 horsepower.
Now, let's talk about horsepower and it's relationship to torque and angular velocity(in the form of revolutions per minute), relative to automotives. Given that power is constant, torque and revolutions per minute will always be inversely proportional. You either have high torque and low RPMs, or low torque and high RPMs.
This can be defined as P = (T * RPM) / 5252, where:
P = Power
T = Torque
RPM = Revolutions per minute
Let's test this out with a few examples. Say your car outputs 100 horsepower at 4000 rpm. Let's to a little bit of basic algebra.
100 = (T * 4000) / 5252
100 * 5252 = T * 4000
(100 * 5252) / 4000 = T
Torque = 131.3ft-lbs
Now, let's say that the vehicle is creating 100 horsepower at 200 rpm.
100 = (T * 200) / 5252
100 * 5252 - T * 200
(100 * 5252) / 200 = T
Torque = 2,626ft-lbs
Notice how between both equations, when the RPM figure is low, the torque figure is quite large, while when the RPM figure is high, the torque is quite low, even though both instances, 100 horsepower is produced.
The reason we divide by 5252 in this equation is because at 5252 RPM, 1ft-lb of torque is equal to 1 HP. In a more technical term, it is the rounded value of 33,000ft-lb/min divided by 2π rad/rev.
With all this in mind, let's talk about the real world, where power is not a constant value in a vehicle.
At a standstill, your vehicle requires relatively massive amounts of torque to get it moving. This is due to your RPM being at idle-speed (roughly 600-1000, depending on the car) and requiring more turning force to begin moving the wheels. Remember, low RPM means proportionately high torque. The more torque your vehicle can produce, the faster you will start accelerating. if you look over the previous equations, you will understand why this is the case.
As vehicle speed picks up and so does rotational speed, torque gains become proportionately low.
This does not mean that as you go faster, your torque figure drops or that once you produce more torque, you move slower. Both these figures will rise higher and higher until max output is reached. It just means that when looking at torque, RPMs and horsepower, more effort is required to move from standstill than to maintain a high vehicle speed.