The 'cosmic teardrop' is essentially the past lightcone of a comoving observer (at rest w.r.t. the CMB) in an Einstein-de Sitter expanding universe, shown in proper-distance, proper-time coordinates.
The teardrop shape is caused by the way that light propagates to us from two directions, starting from the CMB, through the (variable rate) expansion of the intervening space. In the beginning, the expansion rate was so fast that the two wave fronts (propagating locally at c) moved away from us. Around time 4 Gy, the expansion rate slowed down enough to enable the wave fronts to make headway in our direction.
A more enlightening equivalent can be depicted in circular coordinates, shown below for values compatible with the latest cosmological data.
This is essentially the 'cosmic teardrop' drawn inside the cosmological balloon analogy, connecting the wave front positions at progressive circular slices of constant cosmic time. But note that this does not make the radial direction a time coordinate. It is a fictitious extra spatial coordinate, which is a rather complex function of cosmic time and total energy density. It can also be viewed as representing the cosmic scale factor (a) multiplied by the Hubble constant.
The "2 Gy rings" show that the expansion rate was very fast in the beginning, gradually decreasing during the 'middle ages' and then increased again lately. The 46 Gly "pizza slices" represent the observable universe's present spatial dimensions and the total circumference the minimum size of the total universe (200 pi = 627 Gly).
 Note that it assumes that the spatial curvature is positive, just 0.1% off perfectly flat. This is within the limits of present observational errors, which tends towards favoring zero curvature, but still allows a small positive curvature. One can obviously not represent a perfectly flat space as circular, unless you imagine an infinitely large circle.
PS: The above was written very compact and terse, in the hope that the diagrams might convey more than the words, so please ask questions if it is not clear what is going on.