To address this question I need to get something else out of the way first.
Experiments that are designed to obtain a specific kind of interference pattern need to manipulate the light in order to give it one or more particular desired properties.
This may give the student the impression that in order for any interference effect to occur the light must be constrained to have one or more specific properties.
To see that this is a false impression consider the following case: we know the phenomenon of color effects when light is interacting with a very thin film, such as a thin film of of an oily substance floating on water. We see this in broad daylight.
The daylight comes from all directions, it comes from any part of the Sun, it is a continuous spectrum. The partial reflection, partial transmission of the light at the boundaries of the thin film, together with the phenomenon of interference, explains the color effects.
The light has none of the properties usually associated with obtaining interference effect: not temporally coherent, not spatially coherent, not monochromatic.
The explanation: the light that reaches the eye had very little freedom as it interacted with the thin film. The light is in and out of the thin film so fast that it doesn't have to be temporally coherent. So we have that there are no demands on the light source: it doesn't have to be temporally coherent, it doesn't have to be spatially coherent.
In general: if the interference effect that you want to obtain is very specific the light source has to be constrained to specific properties. For example, the most demanding form of interference effect is holography, requiring a light source with very specific properties.
The double slit setup
In the case of a double slit setup the most important factor is spatial coherence.
The incoming light negotiates the first slit, travels, negotiates the double slit, travels again a distance, and hits a photosensitive screen.
The effect of the slits is that on the photosensitive screen the distance that the light has traveled (whatever path it took), is sharply defined. Conversely, without the preliminary single slit there is no sharply defined distance along the traveled path to photosensitive screen. Whether or not there is a sharply defined distance is referred to as 'spatial coherence'.
(If the light source is itself already a point source then the preliminary single slit isn't necessary. The deciding factor is whether there is a sharply defined distance traveled. That is why in astronomy a diffraction grating is sufficient to obtain a spectrum of the light from a star; the star is so distant that it is in effect a point source: spatial coherence)
There is another condition for obtaining an interference pattern. Let's say the setup is scaled up a lot: very large distance between the slits, very large distance to the photosensitive screen. Let's say the light source produces light that is very close to monochromatic at any specific point in time, but the frequency does fluctuate over time. In the scaled up version the time-of-travel from each slit to the photosensitive screen becomes a significant factor. Significant fluctuation on the time scale of the difference of time-of-travel will reduce the definition of the interference pattern. This constraint on fluctuation of the frequency of the light source is referred to as 'temporal coherence'.
