You could be asking yourself the same questions using PCA! Usually these linear transformations (or even non-linear for that matter, PCA, LDA, ICA, UMAP etc.) are used to reduce the high dimensional features space to serve one or multiple purposes. For example in PCA one could use it to compress the high-dimensional feature space to lower (usually 2 or 3) by finding the directions of maximal variance, either for better separation or a simple compression or better explainability via projected visualization for human eyes. Sometimes they are served for better class separation like the case of LDA, in a supervised fashion (in contrast to PCA). In case you missed it check out Sebastian Raschka's post on the difference between LDA and PCA for dimensionality reduction (be careful with LDA assumptions).
In order to answer the question about the axes, we better touch briefly on what LDA is aiming to do, borrowing the explanation from this blog post:
LDA aims to find a new feature space to project the data in order to
maximize classes separability. The first step is to find a way to
measure this capacity of separation of each new feature space
candidate. In 1988, a statistician called Ronald Fisher proposed the
following solution: Maximize the function that represents the
difference between the means, normalized by a measure of the
within-class variability. The Fisher’s propose is basically to
maximize the distance between the mean of each class and minimize the
spreading within the class itself. Thus, we come up with two measures:
the within-class and the between-class.
[The Answer]: As in the case of PCA: the first axis (by convention PCA 1) represents the axis holding the maximum variance in the data, PCA 2 the second in the rank and so forth. The same analogy holds true to LDA. Here though, LDA 1 (your x-axis in the graph, again by convention and the visual judgement) accounts for the maximum variation among the classes, and LDA 2 the second and so forth (still confused, you might one to check this video). You can define a simple linear model to separate them, that is it, that perhaps you couldn't using the original features.
[Bonus]: Although I am finished with the answer, and the following it is not super relevant, but I would like to bring a super nice example what these techniques might be able to answer from data. In the case of, again PCA, Tableau team is showing such capabilities, see this video. In real world problems, not a simple IRIS, these will come handy, and surely these possible even outside Tableau, but requires more efforts.