To order things in ggplot2, you use factors and specify factor levels as the order. The key thing in your example is that you actually want to order your pathways: your y variable (Description), based on your database: your fill variable (ONTOLOGY).

A solution could be to:

1. specify the database (ONTOLOGY) variable as a factor where the levels are the desired order (you could use forcats for this as Mark suggests)
2. arrange your input data by this database factor with dplyr::arrange
3. speficy the pathway (Description) variable as a factor where the levels are the final order in which they are

For example:

# Libraries
library(ggplot2)
library(dplyr)

# Example data
data <- data.frame(
  Description = c("A","E","B","I","O","J","K"),
  ONTOLOGY = c("BP","MF","BP","MF","CC","BP","CC"),
  Count = sample(1:10,7)
)

# Your initial plot
ggplot(data, aes(Count, Description, fill = ONTOLOGY)) + geom_bar(stat = "identity") +
  theme(legend.position = "bottom", axis.title.y = element_blank()) +
  geom_text( aes(label = paste(Count)), color = "black", size = 4, hjust = 0.1, position = position_dodge(0.9) )

# Define the order for the ontology types (BP, MF, CC)
data$ONTOLOGY <- factor(data$ONTOLOGY, levels = rev(c("BP","MF","CC")))

# Arrange the dataframe by the ontology types
data <- dplyr::arrange(data, ONTOLOGY)

# Set the final factor order for the pathways
data$Description <- factor(data$Description, levels = data$Description)

# Final ordered plot
ggplot(data, aes(Count, Description, fill = ONTOLOGY)) + geom_bar(stat = "identity") +
  theme(legend.position = "bottom", axis.title.y = element_blank()) +
  geom_text( aes(label = paste(Count)), color = "black", size = 4, hjust = 0.1, position = position_dodge(0.9) )